Tuesday, April 12, 2011

Kevin Moore didn't do anything special in the last few weeks, that I know of. However, I recently got the latest OSI album, and listening to it the past few days inspired me to make a blog post to introduce readers to this man's amazing music. We'll look at five songs, so if you've got the patience for some great tunes, make sure to read past the jump. Some of these are long, open another browser tab while you listen might be advised.

Kevin Moore was the first keyboardist of Dream Theater, with them for the first three albums. This song, which he wrote the lyrics for, comes from their second, Images and Words. A lot of people who like Dream Theater think this is their best album, and I'm inclined to agree with them. This song can be interpreted on a lot of levels, and even though it feels like it's three parts long, it's only five minutes.

This is the last song he did with Dream Theater - the music and lyrics are both composed by him alone. A few days before they finished recording the album, Kevin told the rest of the band he'd be leaving so he could have more artistic freedom with a solo career. The day after that, he and vocalist James LaBrie recorded this song. If LaBrie's voice sounds different, it's because Moore's is layered in with it - which, amusingly, LaBrie only realized after he heard it on the album. "Kevin Moore saw this photograph in a fashion magazine of a beautiful model wearing a space-dye vest and he fell in love with her," LaBrie said. "He carried that magazine around with him for ages, but he realized that the only way the innocence could be kept, so that he could retain that love for her, was if she stayed on the page. If he'd met her, all that would have been lost."

Sunday, April 10, 2011

This is the continuation of a previous post. In order to deal with more in-depth concepts, I will write for an audience that has read that post. However, a quick recap would not be untoward.

In the previous post, we defined two new truth values, but before them, let's look at the original two. The first, True, applies to statements of which it can be truly said that they are found True, and it can only be falsely said that they are found False. The second, False, applies to statements of which it can be truly said that they are found False, and only falsely said that they are found True. If this seems circular, it is. It's exactly as circular as saying that the traits of a positive number can be indicated by the fact that multiplying a positive by a positive yields a positive, while multiplying a positive by a negative yields a negative (and similarly, that the traits of a negative number can be shown by the fact that a negative multiplied by a positive yields a negative, whilst a negative multiplied by another negative yields, oddly, a positive). These somewhat obliquely stated definitions also serve to indicate that a statement which is found alternately both True and False is belongs neither to the set of properly True statements nor to the set of properly False ones, and similarly that a statement which cannot be found to be either True or False at all belongs to neither set.

Now, let us formally define our two posited complex truth values that supplement True and False. The first we have called Mu, due to the fact that asking whether the statement valued Mu is true or false is a question which ought to be unasked, though the coincidence between that word's first letter and the initial letter of 'maybe' certainly was not a dissuading factor, nor was the fact that its name is the first two letters of 'multiple'. The value Mu applies to statements which can by found to be True when treated as such, and which can equally be found to be False when treated as such. Mu does not fit into the previous paragraph's analogy of integers, because while the statements it applies to are not without disproof nor without proof, likening it to zero would press its etymology beyond the breaking point, for it does not have the properties of that integer, either. Mu's mathematical analogue is best understood in relation to its opposite, Nix.

Just as Mu's name comes from the answer to beautiful koans, the name of Nix, as its opposite, has no such beautiful origins. Though I'm sure if these ideas catch on, some Jungian or Thelemite will come along and replace the middle letter of Nix with a 'y' or an 'o' so that they can wax poetic, its name was chosen simply because, just as V (vrai, French for 'true') and F are one degree of freedom apart in the way they are articulated, so are M and N. A statement's value is Nix if attempts to assess the statement's truth value which start by assuming it to be True find it False, and attempts which start by assuming it to be False find it True. In the previous article, the simplest Empedoclean paradox was used as an example: "This statement is false." If you assume that the statement as a whole is True, you can derive from this truth that what the statement says must be true, and therefore that the statement is False. In mirrored fashion, if you start with the idea that the statement is False, you must interpret that what the statement says must be false in order for it to be false, and thus you arrive at the notion that the statement is True. No, the statement is Nix.

We had best save the mathematical analogy of these two values for the next post in this series, for I fear we have gotten far to abstract for anyone but the logician to see value in continuing forward. Let us then veer away from complex Boolean algebra towards real-life examples of these.

In the previous post, we used the example of Cindy, who has no patience for people who have no patience for her but gets along fine with people who expect the best in her (sound like anyone you know?). We said that, "Cindy is hard to get along with," was Mu, given that the way acceptance or negation of the statement affected one's actions made it self-fulfilling. Similarly, there were studies done where classes of students were given fake aptitude tests where the teachers (sometimes just the teachers, sometimes the students as well) were informed that they were gifted and talented. Whichever students were given those results performed remarkably the rest of the time they were with that teacher. In this case, "Student P has great potential," is a way of expressing the Mu statement. Now let's look at some other places where Mu turns up.

One great place to look for Mu is in the rules of particular perceptual sets or paradigms. For instance, both "The external world is more real than our minds; when we perceive, we perceive it, mediated through our minds," and "The world is what attention is directed to; no external world need be postulated, for we unconsciously account for continuity when we look back at what we've previously attended," are Mu. Same with the statements, "The intricacy of the universe indicates a transcendental being either created it at one point or tailored it to Its liking as time passed," and "The intricacy of the universe indicates that it is transcendent to any being." The same holds for theories of personality, "The personality consists of an aggregation of complexes distributed over unconscious, preconscious, and conscious levels as it unfolds over time," and "The personality has a fiery component (will), a watery component (emotions), an airy component (cognition), an earthy component (sensations and patterns of muscular tension), and an etheric component (the intuition)," are both Mu.

The truth value of these set of statements may have something to do with the way psychology has been treated by the 'hard' sciences. In various essays on the philosophy of science, psychoanalytic theory is disparaged as unfalsifiable pseudoscience and sent away on the same barge that carries away astrology. All of this is done from a paradigm where true and false are the only possibilities, and it makes sense that supporters of such an ontology would find Mu statements anathema. Rather than admitting that there may be another set of statements besides those true or false from all points of reference, we have the game rule that anything that can be shown false at all is false indeed, and any instance of seeing it as true is a result of deception or self-delusion. All this in order to preserve a binary logic.

That's not to say that recognizing some Mu statements for what they are is incompatible with an ultimate worldview where properly phrased statements about the universe are either true or false. For instance, consider the statements "The Sun revolves around the Earth," and "The Earth revolves around the Sun," are both Mu statements. For a long period in human history the first was believed true, then for a shorter period it came to be believed false while the second was believed true, but as our understanding of the relativity of motion developed, we came to realize that the order of things can be just as accurately described from the reference frame of the Earth or that of the Sun. We could even take a reference frame where the Earth is quite stationary, and all the stars revolve around it in the span of a day, and not have an inaccuracy.

What we do for the sake of practicality is to use whichever perspective is convenient to our purposes, but we have discovered a deeper truth in this process: "The motion of the Sun and Earth is such that it can be described by order O from reference frame R and by order P from reference frame S." No one talks like that, though, and with the lack of actual change created by other methods like General Semantics and E-Prime to transform our language to make it accord better with reality, it may be more convenient and accomplish many of the same goals to simply add another truth value to our ontology.

By now you may see the use of Mu in philosophy and interpersonal interaction, but what about Nix? Surely it's confined to logical paradoxes like "The set that contains all sets that do not contain themselves contains itself." Surely we can avoid worrying about Nix and enjoy our lives to the fullest. Perhaps. But consider those experiences that can flit through your mind which vanish as soon as you start thinking about them. Think about how thinking is just another mode of experience, and that it often does quite poorly at describing events that are not mediated through thought. Recall how the ancient sages often speak in paradoxes in order to get across a message that transcends thought. "The name that can be named is not the eternal name."

Next time we'll look at recursion in Grelling's paradox, interpersonal interaction, and paradigms of belief to see why they have Mu statements in common, and we'll start to explore mathematical analogies for all four truth values.

Wednesday, April 6, 2011

I hope you guys enjoyed the April Fools post as much as I enjoyed writing it. The part about finding life in the sub-glacial lakes was true, but I have no knowledge about whether UCLA is planning an expedition, and to my knowledge the 1930s expedition did not occur outside of Lovecraft's novella.

Today I'd like to talk about logic. Symbolic logic is the art of creating a formal system (that is, a system where strings of symbols can have their forms changed according to specific rules) that that matches with specific laws of logic. Aristotle is famed for, among other things, creating an early system of symbolic logic which could parse statements like, "All cats are mammals," and, "All mammals are vertebrates," coming to the conclusion that, "All cats are vertebrates," and, "Some vertebrates are cats," held true while, "All vertebrates are cats," did not. What was so amazing about this was that only rules for organizing symbols were used to come to these conclusions from the premises; of course any human with a left frontal lobe could tell you which conclusions were true and which weren't, but creating a set of rules which tell you this automatically was something worth a bit of bedazzlement.

Any logical problem dealt with a system of premises (things known or accepted as true) and conclusions (things that could be deduced from the premises according to the rules of the formal system), and certain rules were assumed in order to create a system where conclusions could be derived from premises at all. Two of Aristotle's assumptions which have become more contentious in the past few centuries are called the Law of Non-Contradiction and the Law of Excluded Middle.

The Law of Non-Contradiction stated that, in any system of premises and derivable conclusions, there must be no case where both a statement and its negation are both held to be true. For instance, if we had a set of premises that included the statements, "Politicians are in it for the money," and "Politicians want to make the world a better place," we could derive "Politicians are not in it from the money" from the second statement and we'd have a contradiction, which is not allowed per said law. Any logician worth their salt would quickly resolve the issue by adding the word, "Some," to both premises. However, there are some situations where a work-around like this cannot be performed, such as with the premise, "This premise is false." The statement must be false in order for it to be true, so we could derive both, "Premise A is true," and, "Premise A is not true," violating the Law of Non-Contradiction.

The Law of Excluded Middle is a lot like the previous law seen from the other side: it states that in any system there must be no case where both a statement and its negation are both held to be false. In other words, well-formed statements must be true or false, and there is no middle ground (hence the name).

In order to see where this law collapses, we'll have to look at Grelling's paradox. To find this paradox, we create a new word. The first is, 'autological,' and it's define so that a term that is autological if it's definition describes or implies itself. So words like 'pentasyllabic,' 'English,' 'français,' 'sesquipedalian,' and 'last' (being at the end of this list) are all autological, while 'abbreviation,' 'anglais,' 'long,' 'first' (in this case), and 'onomatopoeia' are not. This second list is particularly illustrative of what it means to be the opposite of autological, but more mundane words like 'cat' and 'tarp' are not autological either.

Now, is the word 'autological' itself autological? Since the word implies implying itself, we could safely say that it is, but if we said that it was not, there would be nothing to disprove our assertion, since the word would already have to be assumed to be autological in order to imply itself, itself. That's quite a garble of a sentence, but try it. Assume 'autological' is autological, and any way you can come at the question, your assumption appears true. Assume it's not autological, and your assumption seems just as true. As you can see, this is a case where the Law of Excluded Middle does not apply.

There are various ways logicians have dealt with these two problems, including postulating an 'Indeterminate' truth value aside from 'True' and 'False,' but my favorite way to deal with it is to add two complex truth values to the simple two. The first one I like to call 'Nix,' and it applies to statements like, 'This statement is false,' where whatever you assume in order to evaluate the statement comes up wrong. The second one I call 'Mu,' after the Chinese way of 'unasking' a question - it implies that the question is flawed in that an answer to it must be based on hidden assumptions rather than the quality of the thing itself.

As an example of a 'Mu' statement, consider, 'Cindy is a hard person to get along with.' Now, it may be the case that the Cindy in question here is sensitive to people's expectations, and feels put off when people tense around her. She can be quite friendly when approached with friendliness, but other times she can be a really difficult person. If you approach her with the belief that she's easy-going, she'll mirror your relaxation and you'll find yourself proven right. On the other hand, if you brace yourself for difficulty with her, you're going to have a bad time.

In the next article in this series, we'll talk more about situations where the 'Mu' truth value is useful, about where the names came from, and a bit about Nix's applicability to life. I'd like to end with a quote.

"Love can only thrive within us when we believe in — indeed, unconditionally presuppose — the presence of love within others, from the first moment clear unto the last. Forever the mistrust endemic to nihilism raises the terrible possibility that there is no love within others, and whenever we choose this mistrust, we remove from ourselves the very possibility of finding love. Believe, and we find love, perhaps within others, yet more crucially — more gracefully — within ourselves. The tension between these two possibilities, between which we are eternally poised, lies at the root of existential angst."

Friday, April 1, 2011

So maybe you've heard about the recent Russian expedition in the Antarctic where they found a liquid lake buried deep under the ice. Recently viruses that eat other viruses were found in its waters, and American scientists are preparing an expedition to where they suspect an even larger underground lake may be found, at around 87 degrees South, 116 degrees West. What many do not know is that this expedition will take the team very close to the mountains where all but two of the crew of the 1930-1931 expedition from Massachusetts died.

From what records remain, the little-known expedition landed in Marie Byrd Land (refer to the map above) and trekked towards the the Transantarctic Mountains. The expedition was one of the first where the technology existed for the crew to carry a drill capable of reaching hundreds of feet below the ice. Such drills had existed before, but they were previously too large to carry on a half-year expedition deep into the last continent. From the records geologist William Dyer and his intern returned with, it appears that near the tremendously high foothills of the Transantarctic Range, a hollow chamber was discovered below the ice.

In this cave a great variety of fossils were found, including a wide range of organisms which, on other continents, were only found in separate strata. Samples brought back by Dr. Dyer have since been dated using various radiometric clocks, and it has been found that, rather than the more recent organisms appearing earlier in this region, the more primordial invertebrates flourished for a much longer period here, when they had long gone extinct on other continents.

While this may appear to throw doubt onto the Gondwana hypothesis, a few similar colossal invertebrate fossils from 200 million years ago and before have been found in southern Australia and South America. Religious thinkers opposing evolution tend to ignore the evidence from the 1930-31 expedition due to its being little-known, but it does cast some doubt on the current evolutionary narrative, while not the theory itself.

Dr. William Dyer and a stone relief he discovered, along with a trusty canine companion.

Most interesting of the discoveries on this expedition, which led to many scientists dismissing the entirety of Dr. Dyer's evidence as fraud, were rubbings and photographs of a great number of bas-reliefs the geologist claimed to have found in a 'great city' high in the Transantarctic Range. These images are often used by advocates of the ancient astronaut notion as evidence of their beliefs, though none of the images seem to depict the invertebrate entities arriving from any extraterrestrial origins.

The primary reason for the dismissal of Dr. Dyer's findings was the madness he succumbed to upon his return to civilization. Before he was fully in the throes of paranoid schizophrenia, he claimed that underground expeditions to this region of the frozen continent were prone to mortal danger. He published a record of his journeys in 1931, but the periodical soon went out of print. Since the publication several authors have written fictional narratives of the 1930-31 expedition, most notably Howard Phillips Lovecraft's novel At the Mountains of Madness, which was written quite soon after the article's publication in a rather brief period, but little is known of what Dr. Dyer actually encountered in these regions.

Lovecraft's version of the tale, which has outlived the scientific publication by Dyer himself, incorporates a variety of entities from his other tales. In a 1937 letter soon before his death, the author claimed the geologist allowed him to see a few of his private rubbings in 1932 a few months before Dyer's own death, and that these inspired many of his later stories.

With the coming expedition, headed by staff from UCLA, perhaps we may get to see firsthand what lies in those regions near the Transantarctic Mountains below the glacial plate. Technology has certainly advanced since the expedition of the 1930s, and satellites will allow for data to be directly streamed to the mainland from the expedition crew in real-time. Get ready to tune in in September when the crew arrives at the Ross Ice Shelf.